separation of variables to find the solutions to the differential equations in Problems 1-12, ect to the given initial conditions. -=-2P, P(0)=1 dp p. -=1, P(0)=1 N 2. 4. dm ds L == 2 L(0) = 100 -=m, m(1) = 2

Q: Use integration by parts to evaluate the definite integral Answer: te-t dt.

A: Given  that ∫06te-tdt.To evaluate : the definite integral.Solution :∫fxgxdx=fx∫gxdx-∫f'x∫gxdxdx…

Q: 3ax-4b x-0 cx³-2m Evaluate lim , where a, b, c and m are constants

A: Our Aim is to evluate the limit of the expression given below:-limx→03ax2-4bcx3-2m-(i)

Q: 1. See the attached image for question #1 and answer it  2. What is the degree of N?   a. 0 b. 1…

A: Here is the solution:

Q: 8. 34 S[(x¹y+x²y²)dydx 21 pi/2

A: Since you have asked multiple question, we will solve the first question for you as per our guide…

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A:

Q: After Julia has driven for a quarter of an hour, she was 170 miles east from Denver. After driving…

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Q: Find the volume of the solid obtained by rotating the region bounded by y = 3x², x = 1, x = 4, and…

A:

Q: For each of the following, state whether the equation is ordinary or partial, linear or nonlinear,…

A: as per company guidelines we solve only first three subparts when multiple parts question being…

Q: Given f(x, y) = sin(7xy), find f(x, y) = fy(x, y) =

A: Given; f(x,y)=Sin(7xy).

Q: x2 + 2xy – 4y2)dx – (x² – 8xy – 4y²)dy = 0, Find C when y=1, x=1

A:

Q: After Julia has driven for a quarter of an hour, she was 170 miles east from Denver. After driving…

A:

Q: A particle's velocity is described by the function v(x) = -3cos (t+) where v(t) is measured in…

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Q: Find the average rate of change of the function f(x) = square root x from x1=49 to x2=81

A: We can find the average rate of change of the function in the below steps.

Q: Transform the differential equation y'e yer = 2xy² to FOBDE form. I O dy da O dy da - y = 2xe-y² dy…

A:

Q: 2. Are the planes 2x-y-4z=10 and x-2y+z= 4 parallel or orthogonal?

A:

Q: Find the average rate of change of the function over the given intervals. h(t) = cott a. b. л Зл 4 1…

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Q: 11. Find the sum of the rectangle areas. 14 12 10 8 6 4 2 O 3 f(x)= 6 24 X 6 2

A:

Q: Determine whether the function shown is continuous over the interval (-6,6). Is the given function…

A: To write down that the function is continuous or not in the interval.

Q: Evaluate the integral when x > 0 Answer: [n(x² + + 15x +36) dx.

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Q: Thank you but what about part d: which asks to solve f(1) ?

A:

Q: Let f(x) be the piecewise function -2x + k f(x) = { x² + 1 if x < 1 if x ≥ 1

A: for continuous function

Q: 2. The graphs of f and g are given. Use them to evaluate each limit, if it exists. If the limit does…

A: see below the answer and explanation  as per Bertleby I have to solve first three subparts. For…

Q: Given: (x2 + 2xy - 4y2) dx - (x² - 8xy - 4y2) dy = 0, Find C if y = 1, x = 1 O 1.5 O 2.5 O 3.5 O 4.5…

A: We need to find C.

Q: a) Calculate the derivative of: f(x) = 2³.cos(3x²). sinh(3x + √√x)

A: Since you have asked multiple questions, we will solve the first question for you. If you want any…

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A: Given Price of 4 oranges = $1.72 Christopher spent $1.29

Q: ㅠ Find the surface area of revolution about the x-axis of y = 4 sin (3x) over the interval 0 ≤ x ≤ 3…

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Q: sin(tan-¹(x)) 1+x² dx

A:

Q: 3. y" + 8y' +52y = 26

A:

Q: 6. Consider the function f(x) = 4x³ + 2 i. Find the value of the integral 24x³ + 2 dx ii. Find the…

A:

Q: 23. Find the total area between f(x) and the x-axis where f(x) = + x²-0 on the interval [-1,3].

A:

Q: Let C be the curve 27x-y²=0 between y = 0 and y = 2. Find the area of the surface generated by…

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Q: 1. Find the DE of each of the following by eliminating the arbitrary constants. y = Get + C₂ cosx +…

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Q: Ex)= Sin X -TXX<T Sinodd function cal 2 an=0190-0 f(x) = {busin II X Using the data, I need to…

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Q: 1 decide whether the intermediate value theorem applies to the given function on the indicated…

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Q: Consider the helix r(t) = (cos(-1t), sin(–1t), 3t). Compute, at t= 픔 A. The unit tangent vector T =…

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Q: The points (-3,6), (0,3) and (3,9) lie on the graph of a third degree polynomial function P. If the…

A: The 3rd degree polynomial is  P(x)  Since the points (-3, 6) , (0, 3) and (3, 9) lie on the graph of…

Q: 2. Sketch the graph of the derivative. -10- -8 -6 4 10 8 6 2 -6 -8 10 M 2 6 8 10

A:

Q: 1 Find the first five terms for each of the following recursive sequences. a u₁= -4u, u₁ = 1 -2 U₁ =…

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Q: Eliminate the constants from the following 2x y = x² + С₁e²x + C₂ y' = 2x + 2C₁e²x +3

A:

Q: If the general solution of (2+²-3y2) y'= 2xyżsy"In|y"+xª = Cy", what is the value of b? (A) 3 B 2 -1…

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Q: d 3x²-5 dx 7x+1 +4x²

A: As per Bartleby guideline, we have answered only the first question. If you want to get the answer…

Q: Find f x²+1 √x3+3x+5 dx

A: Solution of given question is written in below steps.

Q: Find the surface area of revolution about the x-axis of y = 6 sin(6x) over the interval 0≤x≤ 96

A:

Q: Determine the solution of the following first-order separable equation: dy 2xy dx = 1+ y²

A: Our Aim is to determine the solution of the following first-order separableequation given…

Q: Find the limit of f(x) = lim_f(x)= 848 (Simplify your answer.) lim_f(x)= 9x 4 8118 (Simplify your…

A: Let's evaluate limit.

Q: Using the following graph of the function f, evaluate the limits (a) through (i) Q 10 8 6 4 -4- 2 6…

A: Given graph of a function f(x)

Q: Find value of Z that maximizes B A = a1 B a2 A¹/3 - a3 Z² A4/3 a4 (Z - 4/1) ² A² a5 1 A3/2

A: The given expression is: BA=a1-a2A13-a3Z2A43-a4Z-A22A2±a51A32

Q: 1) s(x) = 2x − 4/x2 + x − 2

A: As per the company guidelines We can first question only. Please understand. Kindly repost the…

Q: Find all the solutions of the given system of equations using elimination. 0.5x + 0.1y= 0.7 and 0.2x…

A:

Q: Q12: If x + y = 10, then the largest possible Q13:The absolute maximum value of A) has no absolute…

A: Since, we have been asked to solve question-(13) in which our aimis to find the absolute maximum…